as 5milesbaby says above...
There may well be some airspace around that you can turn without any real worry of hitting another aircraft, but not much of it in the UK.
A colleague had to chastise an aircraft the other day in the LTMA as it had asked for a left turn, was told it could not get it due traffic, so proceeded to turn right, straight into the teeth of yet another aircraft. The controller had asked if a right turn would take the aircraft clear, but had not yet authorised it (they were going to have to move other aircraft out of the way to facilitate it).
Fortunately, because of the ongoing communication, the controller in question happened to be looking at the aircraft at the time it turned and thus prevented an airrpox... quite often they will be looking elsewhere.
If you really need to turn and cannot get on ferquency, squawk 7700, it is an attention getter, but bear in mind the controller may well be concentrating on a piece of airspace 100 miles away.
If you have to do this, file an ASR (obviously you'd do that anyways for an emergency squawk).
In fact if at anytime, even in good weather, you find you cannot get on frequency for an inordinate amount of time, file an ASR; too many controllers (and supervisors) forget that service provision is a key factor; once you get several instances of aircraft stepping on each other, then the sector should be split. If that's not possible, then tactical measures should be put in place to slow the traffic flow.
Remember that TCAS is nowhere near as accurate as ground radar, so turning into what you think is a clear piece of airspace may well be more dangerous than continuing towards the CB.
There are other aircraft in the sky who also may be avoiding weather. An unsolicited turn may well mean that they have to be given avoiding action towards the cell they are trying to avoid!
The only way I could think that one may be able to cover oneself legally is to squawk 7700
Turning without permission is not a heinous crime though you need very a good reason to do so. The only legal thing you need to worry about as a pilot is the fact that you are ultimately responsible for the safety of your aircraft.
You can do whatever you want, if you can justify it on safety grounds when you land. Might give us ATCOs a heart attack at the time mind you!